nalgebra/tests/linalg/lu.rs

175 lines
6.1 KiB
Rust

#![cfg_attr(rustfmt, rustfmt_skip)]
use na::Matrix3;
#[test]
fn lu_simple() {
let m = Matrix3::new(
2.0, -1.0, 0.0,
-1.0, 2.0, -1.0,
0.0, -1.0, 2.0);
let lu = m.lu();
assert_eq!(lu.determinant(), 4.0);
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
#[test]
fn lu_simple_with_pivot() {
let m = Matrix3::new(
0.0, -1.0, 2.0,
-1.0, 2.0, -1.0,
2.0, -1.0, 0.0);
let lu = m.lu();
assert_eq!(lu.determinant(), -4.0);
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
#[cfg(feature = "arbitrary")]
mod quickcheck_tests {
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
use std::cmp;
use na::{DMatrix, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5, DVector, Vector4};
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
quickcheck! {
fn lu(m: DMatrix<$scalar>) -> bool {
let mut m = m;
if m.len() == 0 {
m = DMatrix::<$scalar>::new_random(1, 1);
}
let m = m.map(|e| e.0);
let lu = m.clone().lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
relative_eq!(m, lu, epsilon = 1.0e-7)
}
fn lu_static_3_5(m: Matrix3x5<$scalar>) -> bool {
let m = m.map(|e| e.0);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
relative_eq!(m, lu, epsilon = 1.0e-7)
}
fn lu_static_5_3(m: Matrix5x3<$scalar>) -> bool {
let m = m.map(|e| e.0);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
relative_eq!(m, lu, epsilon = 1.0e-7)
}
fn lu_static_square(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
relative_eq!(m, lu, epsilon = 1.0e-7)
}
fn lu_solve(n: usize, nb: usize) -> bool {
if n != 0 && nb != 0 {
let n = cmp::min(n, 50); // To avoid slowing down the test too much.
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
let lu = m.clone().lu();
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
let sol1 = lu.solve(&b1);
let sol2 = lu.solve(&b2);
return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
}
return true;
}
fn lu_solve_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let lu = m.lu();
let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
let sol1 = lu.solve(&b1);
let sol2 = lu.solve(&b2);
return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
}
fn lu_inverse(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
let mut l = m.lower_triangle();
let mut u = m.upper_triangle();
// Ensure the matrix is well conditioned for inversion.
l.fill_diagonal(na::one());
u.fill_diagonal(na::one());
let m = l * u;
let m1 = m.clone().lu().try_inverse().unwrap();
let id1 = &m * &m1;
let id2 = &m1 * &m;
return id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5);
}
fn lu_inverse_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let lu = m.lu();
if let Some(m1) = lu.try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
}
else {
true
}
}
}
}
}
);
gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);
}